Algebraic numbers

 

In Macsyma

For comparison with other CAS choose from: Axiom Derive Maple Mathematica Reduce

inputs outputs

• an algebraic number

  
  algebraic:true;

   
       				      true

  tellrat(sqrt2**2-2);

   
  					2
       				  [sqrt2  - 2]

  rat(1/(sqrt2+1));

   
      /R/ 			   sqrt2 - 1

  ogcd:gcd;

   
       				     spmod

  gcd:'algebraic;

   
       				   algebraic

  rat((x**2+2*sqrt2*x+2)/(x+sqrt2));

   
      /R/ 			   x + sqrt2

  rat((x**3+(sqrt2-2)*x**2-(2*sqrt2+3)*x-3*sqrt2)/(x**2-2));

   
  				   2
  				  x  - 2 x - 3
      /R/ 			  ------------
  				   x - sqrt2

  gcd:ogcd;

   
       				     spmod

  radcan(sqrt(x**2-2*sqrt2*x*y+2*y**2));

   
  				 2		    2
        			 sqrt(2 y  - 2 sqrt2 x y + x )

  untellrat(sqrt2);

   
        				       []

• multiple algebraic extensions

  
  tellrat(sqrt5**2-5,cbrt3**3-3);

   
  				  3	      2
        			    [cbrt3  - 3, sqrt5  - 5]

  rat(cbrt3**3);

   
       /R/ 			       3

  rat(sqrt5**2);

   
       /R/ 			       5

  rat(cbrt3);

   
       /R/ 			     cbrt3

  rat(sqrt5);

   
       /R/ 			     sqrt5

  radcan(sqrt(x**2+2*(sqrt5-cbrt3)*x+5-2*sqrt5*cbrt3+cbrt3**2));

   
  	       2					        2
        	 sqrt(x  + (2 sqrt5 - 2 cbrt3) x - 2 cbrt3 sqrt5 + cbrt3  + 5)

  untellrat(sqrt5,cbrt3);

   
        				       []